Solving asymmetric variational inequalities via convex optimization
Operations Research Letters
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An interior point (IP) method is proposed to solve variational inequality problems for monotone functions and polyhedral sets. The method has the following advantages: 1. Given an initial interior feasible solution with duality gap $\mu_0$, the algorithm requires at most $O[n\log(\mu_0/\ep)]$ iterations to obtain an ep-optimal solution. 2. The rate of convergence of the duality gap is q-quadratic. 3. At each iteration, a long-step improvement is allowed. 4. The algorithm can automatically transfer from a linear mode to a quadratic mode to accelerate the local convergence.